The former Port Vale man is available on a free transfer and featured in a friendly with Queen's Park on Saturday.
"I've been in contact with Sky Sports over the last couple of weeks and got fixed up with Rob Shields," McGregor told Sky Sports News.
"He gave me a ring and got a week's training up at Hamilton, who are obviously a new SPL club, which I thought was a great opportunity to get myself up here training and have a game.
"I will just prepare as I have done in the last 10 or 12 years as a professional footballer and hope Billy sees enough to take a chance on me.
"I will just take every day as it comes."